You can hide the relationship fields by going to the respective layouts and removing them (drag and drop in the recycle bin on the layout screen.) Although I admit, I don't really understand why you would create a relationship and then keep it hidden - if it's hidden, how are the account and opportunity going to get linked? But that's besides the point in terms of answering your question I suppose

You can delete any of the standard reports, or change the Teams setting for a report to just the admin user if you want to hide them from users.

There already exists a relationship between accounts and opportunities (one-to-many).

But in order to make a specific calculation in some fields work I had to create a one-to-one realtionship in addition to that. As a result I had two related fields for Opportunities in the Accounts screen, and two related fields for Accounts in the Opportunities. Now I am wondering if it makes sense to keep both. Do you think removing these will cause any issues or problems?

I don't think I understand enough about what you are trying to do to give you advice. If you hide the extra relationship fields, I'm not sure whether your calculation that relies on them would continue to work or not. My best advice would be to try removing them and see if it works or not. You can always put them back on the layout later if you need them there.